We consider a mean-field Hamiltonian [1]}, [2]} for each of the four \(\sigma \)  flavours with two sublattices \(A_1\)  and \(B_N\) , and order parameter \(\Delta = 2|w|\)  due to the exchange interaction \(w\)  which breaks sublattice symmetry:
\(H_2 = \left(\begin{array}{cc}E_0 + w & -\gamma _1 (- \kappa ^{\dagger })^N \\-\gamma _1 (- \kappa )^N & E_0 - w \\\end{array}\right) , \) 
